A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5cm and the total wood used in the making of toy is 166 5/6cm³. Find the height of the toy. Also, find the cost of painting the hemi-spherical part of the toy at the rate of ₹ 10 per cm². (use π = 22/7).

Explanation below.

Step-by-step explanation:

Given: Radius of hemisphere = radius of cone = r = 3.5 cm

Volume of total wood used in making a toy = 166 ⅚ = 1001/6 cm³

Let h be height of a cone.

Volume of total wood used in making a toy = volume of hemisphere + volume of cone

(⅔) * πr³ + (⅓) π²h

= (⅓) πr² (2r + h)

1001/6 = (⅓) * (22/7) * (3.5) ² * (h + 2*3.5)

1001/6 = (⅓) * (22/7) * 3.5 * 3.5 * (h+7)

1001/6 = (⅓) * 22 *.5 * 3.5 * (h + 7)

1001 * 3 = 6 * 22 *.5 * 3.5 * (h+7)

h + 7 = 1001 * 3 / (6 * 22 *.5 * 3.5)

h + 7 = 1001 * 3 / 132 * 1.75

h + 7 = 1001 * 3 * 100 / 132 * 175

h + 7 = 91 * 3 * 4 / 12 * 7

h + 7 = 91 * 12 / 12*7

h + 7 = 13

h + 7 = 13 - 7 = 6

Height of a cone (h) = 6

Height of the toy = Height of a cone + Height of a hemisphere

Height of the toy = 6 + 3.5 = 9.5 cm

Curved surface area of hemisphere = 2πr²

CSA of hemisphere = 2 * (22/7) * 3.5 * 3.5

= 2 * 22 *.5 * 3.5 = 44 * 1.75 = 77 cm²

Rate of painting the hemispherical part of the toy = ₹ 10 per m².

Cost of painting the hemispherical part of the toy = 77 * 10 = ₹ 770.

Hence, the Height of the toy is 9.5 m & Cost of painting the hemispherical part of the toy is ₹ 770.